计算数学
       首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  在线办公 | 
计算数学  2017, Vol. 39 Issue (1): 59-69    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles  
一类新的(2n-1)点二重动态逼近细分
张莉, 孙燕, 檀结庆, 时军
合肥工业大学数学学院, 合肥 230009
A NEW FAMILY OF (2n-1)-POINT BINARY NON-STATIONARY APPROXIMATING SUBDIVISION SCHEMES
Zhang Li, Sun Yan, Tan Jieqing, Shi Jun
School of Mathematics, Hefei University of Technology, Hefei 230009, China
 全文: PDF (863 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 利用正弦函数构造了一类新的带有形状参数ω的left(2n-1right)点二重动态逼近细分格式.从理论上分析了随n值变化时这类细分格式的Ck连续性和支集长度;算法的一个特色是随着细分格式中参数ω的取值不同,相应生成的极限曲线的表现张力也有所不同,而且这一类算法所对应的静态算法涵盖了Chaikin,Hormann,Dyn,Daniel和Hassan的算法.文末附出大量数值实例,在给定相同的初始控制顶点,且极限曲线达到同一连续性的前提下和现有几种算法做了比较,数值实例表明这类算法生成的极限曲线更加饱满,表现力更强.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词动态细分格式   逼近细分   正弦函数   形状参数     
Abstract: In this paper,a new family of (2n-1)-point binary non-stationary approximating subdivision schemes with shape parameter ω is presented with the help of the sine function.With the changing of n and ω,the theoretical analysis of support length and continuities of the schemes are also given.The corresponding stationary schemes include the methods given by Chaikin,Hormann,Dyn,Daniel and Hassan.With the same control points and the same continuities for the limit curves,comparisons with other methods are given.It shows that the new family of schemes can generate limit curves with better representability than the others.
Key wordsNon-stationary subdivision scheme   Approximating   Sine function   Shape parameter   
收稿日期: 2016-01-12;
基金资助:

国家自然科学基金重点项目(U1135003);国家自然科学基金(61472466,61100126);中国博士后科学基金面上资助项目(2015M571926);浙江大学CAD、CG国家重点实验室开放课题(A1607).

引用本文:   
. 一类新的(2n-1)点二重动态逼近细分[J]. 计算数学, 2017, 39(1): 59-69.
. A NEW FAMILY OF (2n-1)-POINT BINARY NON-STATIONARY APPROXIMATING SUBDIVISION SCHEMES[J]. Mathematica Numerica Sinica, 2017, 39(1): 59-69.
 
[1] Chaikin G M. An algorithm for high speed curve generation[J]. Comput. Graph. Image Process, 1974, 3(4):346-349.
[2] Hormann K, Sabin M A. A family of subdivision schemes with cubic precision[J]. Comput. Aided Geomet. Des. 2008, 25(1):41-52.
[3] Dyn N, Floater M S, Hormann K. A C2 four-point subdivision scheme with fourth order accuracy and its extensions[J]. in:M. Daehlen, K. Morkenm, L.L. Schumaker (Eds.), Mathematical Methods for Curves and Surfaces:Troms 2004, Modern Methods in Mathematics, Nashboro Press, Brentwood, Tenn, USA, 2005, pp. 145-156.
[4] Tan J Q, Yao Y G, Cao H J. Convexity preservation of five-point binary subdivision scheme with a parameter[J]. Appl. Math. Comput. 2014, 245:279-288.
[5] Dyn N, Gregory J A, Levin D. A four-point interpolatory subdivision scheme for curve design[J]. Comput. Aided Geomet. Des. 1987, 4(4):257-268.
[6] 亓万锋, 罗钟铉, 樊鑫. 基于逼近型细分的诱导细分格式[J]. 中国科学, 2014, 44(7):755-768.
[7] 邓重阳, 汪国昭. 曲线插值的一种保凸细分方法[J]. 计算机辅助设计与图形学学报, 2009, 21(8):1042-1046.
[8] Deng C Y, Wang G Z. Incenter subdivision scheme for curve interpolation[J]. Comput. Aided Geomet. Des. 2010, 27(1):48-59.
[9] Deng C Y, Ma W Y. Matching admissible G2 Hermite data by a biarc-based subdivision scheme[J]. Comput. Aided Geomet. Des. 2012, 29(6):363-378.
[10] 刘秀平, 李宝军, 苏志勋, 郁博文. 插值细分曲线有理参数点的精确求值[J]. 计算数学, 2009, 31(3):253-260. 浏览
[11] Deng C Y, Ma W Y. Efficient evaluation of subdivision schemes with polynomial reproduction property[J]. J. Comput. Appl. Math. 2016, 294(C):403-412.
[12] Schaefer S, Warren J. Exact evaluation of limits and tangents for non-polynomial subdivision schemes[J]. Comput. Aided Geom. Design, 2008, 25(8):607-620.
[13] Dyn N, Levin D. Analysis of asymptotically equivalent binary subdivision schemes[J]. J. Math. Anal. Appl. 1995, 193(2):594-621.
[14] Jena M K, Shunmugaraj P, Das P C. A non-stationary subdivision scheme for curve interpolation[J]. ANZIAM J. 2003, 44(E):E216-E235.
[15] Daniel S, Shunmugaraj P. Three point stationary and non-stationary subdivision schemes[C]//3rd International Conference on Geometric Modeling, Imaging. IEEE, 2008:3-8.
[16] Fang M E, Ma W Y, Wang G Z. A generalized curve subdivision scheme of arbitrary order with a tension parameter[J]. Comput. Aided Geomet. Des. 2010, 27(9):720-733.
[17] 庄兴龙, 檀结庆. 五点二重逼近细分法[J]. 图学学报, 2012, 33(5):57-61.
[18] Siddiqi S S, Rehan K. Modified form of binary and ternary 3-point subdivision schemes[J]. Appl. Math. Comput. 2010, 216(3):970-982.
[19] Siddiqi S S, Salam W, Rehan K. Binary 3-point and 4-point non-stationary subdivision schemes using hyperbolic function[J]. Appl. Math. Comput. 2015, 258(C):120-129.
[20] Cao H J, Tan J Q. A binary five-point relaxation subdivision scheme[J]. J. Inf. Comput. Sci. 2013, 10(18):5903-5910.
[21] Mustafa G, Ghaffar A, Bari M. (2n-1)-point binary approximating scheme[C]//Digital Information Management (ICDIM), 2013 Eighth International Conference on. IEEE, 2013:363-368.
[22] Dyn N, Levin D. Subdivision schemes in geometric modeling[J]. Acta Numerica, 2002, 11:73-144.
[23] Hassan M F, Dodgson N A. Ternary and three-point univariate subdivision schemes[J]. In:Albert Cohen, Jean-Louis Merrien, Larry L. Schumaker (Eds.), Curve and Surface Fitting:Sant-Malo 2002, Nashboro Press, Brentwood, 2003, pp. 199-208.
[1] 熊建, 郭清伟. 广义Wang-Ball曲线[J]. 计算数学, 2013, 34(3): 187-195.
[2] 熊建, 郭清伟. 广义Said-Ball曲线[J]. 计算数学, 2012, (1): 32-40.
[3] 刘植, 陈晓彦, 江平, 张莉. 基于函数值的线性有理插值样条的区域控制[J]. 计算数学, 2011, 33(4): 367-372.
[4] 熊建, 郭清伟, 朱功勤. 可整体或局部调控的C3, C4连续的插值曲线[J]. 计算数学, 2011, 32(3): 165-173.
[5] 吴荣军, 彭国华, 罗卫民. 一类带参 B 样条曲线的形状分析[J]. 计算数学, 2010, 32(4): 349-360.

Copyright 2008 计算数学 版权所有
中国科学院数学与系统科学研究院 《计算数学》编辑部
北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发
技术支持: 010-62662699 E-mail:support@magtech.com.cn
京ICP备05002806号-10